TSTP Solution File: SWC020+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SWC020+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed May 31 12:38:54 EDT 2023
% Result : Theorem 0.12s 0.35s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 19
% Syntax : Number of formulae : 87 ( 11 unt; 0 def)
% Number of atoms : 253 ( 49 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 264 ( 98 ~; 98 |; 41 &)
% ( 15 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 14 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 40 (; 30 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [U] :
( ssList(U)
=> frontsegP(U,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,axiom,
! [U] :
( ssList(U)
=> frontsegP(U,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,axiom,
! [U] :
( ssList(U)
=> ( frontsegP(nil,U)
<=> nil = U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( V != X
| U != W
| ? [Y] :
( ssList(Y)
& neq(Y,nil)
& frontsegP(V,Y)
& frontsegP(U,Y) )
| ( nil = V
& nil = U )
| ( ( nil != X
| nil != W )
& ( ~ neq(W,nil)
| ~ frontsegP(X,W) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( V != X
| U != W
| ? [Y] :
( ssList(Y)
& neq(Y,nil)
& frontsegP(V,Y)
& frontsegP(U,Y) )
| ( nil = V
& nil = U )
| ( ( nil != X
| nil != W )
& ( ~ neq(W,nil)
| ~ frontsegP(X,W) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f285,plain,
! [U] :
( ~ ssList(U)
| frontsegP(U,U) ),
inference(pre_NNF_transformation,[status(esa)],[f42]) ).
fof(f286,plain,
! [X0] :
( ~ ssList(X0)
| frontsegP(X0,X0) ),
inference(cnf_transformation,[status(esa)],[f285]) ).
fof(f294,plain,
! [U] :
( ~ ssList(U)
| frontsegP(U,nil) ),
inference(pre_NNF_transformation,[status(esa)],[f45]) ).
fof(f295,plain,
! [X0] :
( ~ ssList(X0)
| frontsegP(X0,nil) ),
inference(cnf_transformation,[status(esa)],[f294]) ).
fof(f296,plain,
! [U] :
( ~ ssList(U)
| ( frontsegP(nil,U)
<=> nil = U ) ),
inference(pre_NNF_transformation,[status(esa)],[f46]) ).
fof(f297,plain,
! [U] :
( ~ ssList(U)
| ( ( ~ frontsegP(nil,U)
| nil = U )
& ( frontsegP(nil,U)
| nil != U ) ) ),
inference(NNF_transformation,[status(esa)],[f296]) ).
fof(f298,plain,
! [X0] :
( ~ ssList(X0)
| ~ frontsegP(nil,X0)
| nil = X0 ),
inference(cnf_transformation,[status(esa)],[f297]) ).
fof(f415,plain,
? [U] :
( ssList(U)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X] :
( ssList(X)
& V = X
& U = W
& ! [Y] :
( ~ ssList(Y)
| ~ neq(Y,nil)
| ~ frontsegP(V,Y)
| ~ frontsegP(U,Y) )
& ( nil != V
| nil != U )
& ( ( nil = X
& nil = W )
| ( neq(W,nil)
& frontsegP(X,W) ) ) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f97]) ).
fof(f416,plain,
! [W,X] :
( pd0_0(X,W)
=> ( nil = X
& nil = W ) ),
introduced(predicate_definition,[f415]) ).
fof(f417,plain,
? [U] :
( ssList(U)
& ? [V] :
( ssList(V)
& ? [W] :
( ssList(W)
& ? [X] :
( ssList(X)
& V = X
& U = W
& ! [Y] :
( ~ ssList(Y)
| ~ neq(Y,nil)
| ~ frontsegP(V,Y)
| ~ frontsegP(U,Y) )
& ( nil != V
| nil != U )
& ( pd0_0(X,W)
| ( neq(W,nil)
& frontsegP(X,W) ) ) ) ) ) ),
inference(formula_renaming,[status(thm)],[f415,f416]) ).
fof(f418,plain,
( ssList(sk0_47)
& ssList(sk0_48)
& ssList(sk0_49)
& ssList(sk0_50)
& sk0_48 = sk0_50
& sk0_47 = sk0_49
& ! [Y] :
( ~ ssList(Y)
| ~ neq(Y,nil)
| ~ frontsegP(sk0_48,Y)
| ~ frontsegP(sk0_47,Y) )
& ( nil != sk0_48
| nil != sk0_47 )
& ( pd0_0(sk0_50,sk0_49)
| ( neq(sk0_49,nil)
& frontsegP(sk0_50,sk0_49) ) ) ),
inference(skolemization,[status(esa)],[f417]) ).
fof(f419,plain,
ssList(sk0_47),
inference(cnf_transformation,[status(esa)],[f418]) ).
fof(f420,plain,
ssList(sk0_48),
inference(cnf_transformation,[status(esa)],[f418]) ).
fof(f423,plain,
sk0_48 = sk0_50,
inference(cnf_transformation,[status(esa)],[f418]) ).
fof(f424,plain,
sk0_47 = sk0_49,
inference(cnf_transformation,[status(esa)],[f418]) ).
fof(f425,plain,
! [X0] :
( ~ ssList(X0)
| ~ neq(X0,nil)
| ~ frontsegP(sk0_48,X0)
| ~ frontsegP(sk0_47,X0) ),
inference(cnf_transformation,[status(esa)],[f418]) ).
fof(f426,plain,
( nil != sk0_48
| nil != sk0_47 ),
inference(cnf_transformation,[status(esa)],[f418]) ).
fof(f427,plain,
( pd0_0(sk0_50,sk0_49)
| neq(sk0_49,nil) ),
inference(cnf_transformation,[status(esa)],[f418]) ).
fof(f428,plain,
( pd0_0(sk0_50,sk0_49)
| frontsegP(sk0_50,sk0_49) ),
inference(cnf_transformation,[status(esa)],[f418]) ).
fof(f429,plain,
! [W,X] :
( ~ pd0_0(X,W)
| ( nil = X
& nil = W ) ),
inference(pre_NNF_transformation,[status(esa)],[f416]) ).
fof(f430,plain,
! [X0,X1] :
( ~ pd0_0(X0,X1)
| nil = X0 ),
inference(cnf_transformation,[status(esa)],[f429]) ).
fof(f431,plain,
! [X0,X1] :
( ~ pd0_0(X0,X1)
| nil = X1 ),
inference(cnf_transformation,[status(esa)],[f429]) ).
fof(f432,plain,
( spl0_0
<=> nil = sk0_48 ),
introduced(split_symbol_definition) ).
fof(f434,plain,
( nil != sk0_48
| spl0_0 ),
inference(component_clause,[status(thm)],[f432]) ).
fof(f435,plain,
( spl0_1
<=> nil = sk0_47 ),
introduced(split_symbol_definition) ).
fof(f437,plain,
( nil != sk0_47
| spl0_1 ),
inference(component_clause,[status(thm)],[f435]) ).
fof(f438,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f426,f432,f435]) ).
fof(f439,plain,
( spl0_2
<=> pd0_0(sk0_50,sk0_49) ),
introduced(split_symbol_definition) ).
fof(f440,plain,
( pd0_0(sk0_50,sk0_49)
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f439]) ).
fof(f442,plain,
( spl0_3
<=> neq(sk0_49,nil) ),
introduced(split_symbol_definition) ).
fof(f443,plain,
( neq(sk0_49,nil)
| ~ spl0_3 ),
inference(component_clause,[status(thm)],[f442]) ).
fof(f445,plain,
( spl0_2
| spl0_3 ),
inference(split_clause,[status(thm)],[f427,f439,f442]) ).
fof(f446,plain,
( spl0_4
<=> frontsegP(sk0_50,sk0_49) ),
introduced(split_symbol_definition) ).
fof(f447,plain,
( frontsegP(sk0_50,sk0_49)
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f446]) ).
fof(f449,plain,
( spl0_2
| spl0_4 ),
inference(split_clause,[status(thm)],[f428,f439,f446]) ).
fof(f482,plain,
( spl0_5
<=> ssList(nil) ),
introduced(split_symbol_definition) ).
fof(f484,plain,
( ~ ssList(nil)
| spl0_5 ),
inference(component_clause,[status(thm)],[f482]) ).
fof(f485,plain,
( spl0_6
<=> nil = nil ),
introduced(split_symbol_definition) ).
fof(f488,plain,
( ~ ssList(nil)
| nil = nil
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f298,f295]) ).
fof(f489,plain,
( ~ spl0_5
| spl0_6 ),
inference(split_clause,[status(thm)],[f488,f482,f485]) ).
fof(f492,plain,
( $false
| spl0_5 ),
inference(forward_subsumption_resolution,[status(thm)],[f484,f223]) ).
fof(f493,plain,
spl0_5,
inference(contradiction_clause,[status(thm)],[f492]) ).
fof(f494,plain,
( pd0_0(sk0_48,sk0_49)
| ~ spl0_2 ),
inference(forward_demodulation,[status(thm)],[f423,f440]) ).
fof(f495,plain,
( pd0_0(sk0_48,sk0_47)
| ~ spl0_2 ),
inference(forward_demodulation,[status(thm)],[f424,f494]) ).
fof(f496,plain,
( nil = sk0_47
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f495,f431]) ).
fof(f497,plain,
( nil = sk0_48
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f495,f430]) ).
fof(f498,plain,
( $false
| spl0_0
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f497,f434]) ).
fof(f499,plain,
( spl0_0
| ~ spl0_2 ),
inference(contradiction_clause,[status(thm)],[f498]) ).
fof(f500,plain,
( neq(sk0_47,nil)
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f424,f443]) ).
fof(f501,plain,
( frontsegP(sk0_48,sk0_49)
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f423,f447]) ).
fof(f502,plain,
( frontsegP(sk0_48,sk0_47)
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f424,f501]) ).
fof(f505,plain,
( spl0_7
<=> ssList(sk0_47) ),
introduced(split_symbol_definition) ).
fof(f507,plain,
( ~ ssList(sk0_47)
| spl0_7 ),
inference(component_clause,[status(thm)],[f505]) ).
fof(f508,plain,
( spl0_8
<=> neq(sk0_47,nil) ),
introduced(split_symbol_definition) ).
fof(f510,plain,
( ~ neq(sk0_47,nil)
| spl0_8 ),
inference(component_clause,[status(thm)],[f508]) ).
fof(f511,plain,
( spl0_9
<=> frontsegP(sk0_47,sk0_47) ),
introduced(split_symbol_definition) ).
fof(f513,plain,
( ~ frontsegP(sk0_47,sk0_47)
| spl0_9 ),
inference(component_clause,[status(thm)],[f511]) ).
fof(f514,plain,
( ~ ssList(sk0_47)
| ~ neq(sk0_47,nil)
| ~ frontsegP(sk0_47,sk0_47)
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f425,f502]) ).
fof(f515,plain,
( ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_4 ),
inference(split_clause,[status(thm)],[f514,f505,f508,f511,f446]) ).
fof(f516,plain,
( spl0_10
<=> neq(nil,nil) ),
introduced(split_symbol_definition) ).
fof(f522,plain,
( spl0_12
<=> ssList(sk0_48) ),
introduced(split_symbol_definition) ).
fof(f524,plain,
( ~ ssList(sk0_48)
| spl0_12 ),
inference(component_clause,[status(thm)],[f522]) ).
fof(f535,plain,
( spl0_15
<=> frontsegP(sk0_48,nil) ),
introduced(split_symbol_definition) ).
fof(f537,plain,
( ~ frontsegP(sk0_48,nil)
| spl0_15 ),
inference(component_clause,[status(thm)],[f535]) ).
fof(f538,plain,
( ~ ssList(nil)
| ~ neq(nil,nil)
| ~ frontsegP(sk0_48,nil)
| ~ ssList(sk0_47) ),
inference(resolution,[status(thm)],[f425,f295]) ).
fof(f539,plain,
( ~ spl0_5
| ~ spl0_10
| ~ spl0_15
| ~ spl0_7 ),
inference(split_clause,[status(thm)],[f538,f482,f516,f535,f505]) ).
fof(f545,plain,
( $false
| spl0_1
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f496,f437]) ).
fof(f546,plain,
( spl0_1
| ~ spl0_2 ),
inference(contradiction_clause,[status(thm)],[f545]) ).
fof(f554,plain,
( ~ ssList(sk0_48)
| spl0_15 ),
inference(resolution,[status(thm)],[f537,f295]) ).
fof(f555,plain,
( $false
| spl0_15 ),
inference(forward_subsumption_resolution,[status(thm)],[f554,f420]) ).
fof(f556,plain,
spl0_15,
inference(contradiction_clause,[status(thm)],[f555]) ).
fof(f567,plain,
( $false
| spl0_12 ),
inference(forward_subsumption_resolution,[status(thm)],[f524,f420]) ).
fof(f568,plain,
spl0_12,
inference(contradiction_clause,[status(thm)],[f567]) ).
fof(f584,plain,
( $false
| spl0_7 ),
inference(forward_subsumption_resolution,[status(thm)],[f419,f507]) ).
fof(f585,plain,
spl0_7,
inference(contradiction_clause,[status(thm)],[f584]) ).
fof(f586,plain,
( ~ ssList(sk0_47)
| spl0_9 ),
inference(resolution,[status(thm)],[f513,f286]) ).
fof(f587,plain,
( ~ spl0_7
| spl0_9 ),
inference(split_clause,[status(thm)],[f586,f505,f511]) ).
fof(f588,plain,
( $false
| ~ spl0_3
| spl0_8 ),
inference(forward_subsumption_resolution,[status(thm)],[f510,f500]) ).
fof(f589,plain,
( ~ spl0_3
| spl0_8 ),
inference(contradiction_clause,[status(thm)],[f588]) ).
fof(f590,plain,
$false,
inference(sat_refutation,[status(thm)],[f438,f445,f449,f489,f493,f499,f515,f539,f546,f556,f568,f585,f587,f589]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SWC020+1 : TPTP v8.1.2. Released v2.4.0.
% 0.03/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue May 30 11:40:22 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % Drodi V3.5.1
% 0.12/0.35 % Refutation found
% 0.12/0.35 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.23/0.57 % Elapsed time: 0.020332 seconds
% 0.23/0.57 % CPU time: 0.049964 seconds
% 0.23/0.57 % Memory used: 16.179 MB
%------------------------------------------------------------------------------